Newbetuts

Showing that $\displaystyle\limsup_{n\to\infty}x_n=\sup\{\text{cluster points of $\{x_n\}_{n=1}^\infty$}\}$

Defining the Derivative using Internal Set Theory (Non Standard Analysis)

I am confused at a step in the proof of Cauchy Criterion otherwise known as Cauchy Condensation

$x_{n+1}=-1+\sqrt[n]{1+nx_n}$, $x_1>0$ limits

Every bounded monotone sequence converges

Prove that a degree-$6$ polynomial has exactly $2$ real roots

Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?

How to prove that $ {\mathbf{GL}_{n}}(\mathbb{R}) $ is dense in $ {\mathbf{M}_{n}}(\mathbb{R}) $

Is indefinite integration suspect?

Functional Equation of Rectangular Graphs

A continuous function, with discontinuous derivative, but the limit must exist.

Limit of $S(n) = \sum_{k=1}^{\infty} \left(1 - \prod_{j=1}^{n-1}\left(1-\frac{j}{2^k}\right)\right)$ - Part II

Proving Nonhomogeneous ODE is Bounded

Does the sum $\sum\limits^{\infty}_{k=1} \frac{\sin(kx)}{k^{\alpha}}$ converge for $\alpha > \frac{1}{2}$ and $x \in [0,2 \pi]$?

product rule for matrix functions?

Is every Riemann-integrable function lebesgue integrable?

Convergence of $\sum_{n=0}^{\infty} \left(\frac{1+\frac 12+\ldots+\frac 1n}{n}\right)^p$

New posts in real-analysis

How to show $\sqrt{4+2\sqrt{3}}-\sqrt{3} = 1$

Why dense subsets are convenient to prove theorems

Are there any different proof of the uncountability of $[0, 1]$?

Showing that $\displaystyle\limsup_{n\to\infty}x_n=\sup\{\text{cluster points of $\{x_n\}_{n=1}^\infty$}\}$

Defining the Derivative using Internal Set Theory (Non Standard Analysis)

I am confused at a step in the proof of Cauchy Criterion otherwise known as Cauchy Condensation

$x_{n+1}=-1+\sqrt[n]{1+nx_n}$, $x_1>0$ limits

Every bounded monotone sequence converges

Prove that a degree-$6$ polynomial has exactly $2$ real roots

Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?

How to prove that $ {\mathbf{GL}_{n}}(\mathbb{R}) $ is dense in $ {\mathbf{M}_{n}}(\mathbb{R}) $

Is indefinite integration suspect?

Functional Equation of Rectangular Graphs

A continuous function, with discontinuous derivative, but the limit must exist.

Limit of $S(n) = \sum_{k=1}^{\infty} \left(1 - \prod_{j=1}^{n-1}\left(1-\frac{j}{2^k}\right)\right)$ - Part II

Proving Nonhomogeneous ODE is Bounded

Does the sum $\sum\limits^{\infty}_{k=1} \frac{\sin(kx)}{k^{\alpha}}$ converge for $\alpha > \frac{1}{2}$ and $x \in [0,2 \pi]$?

product rule for matrix functions?

Is every Riemann-integrable function lebesgue integrable?

Convergence of $\sum_{n=0}^{\infty} \left(\frac{1+\frac 12+\ldots+\frac 1n}{n}\right)^p$